Performance Analysis of CSMA/CA and PCA for Time Critical Industrial IoT Applications

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1 This article has been accepted for publication in a future issue of this journal, but has not been fully edited. Content may change prior to final publication. Citation information: DOI.9/TII , IEEE Performance Analysis of CMA/CA and for Time Critical Industrial IoT Applications M. P. R.. Kiran and P. Rajalakshmi Abstract Recently proposed IEEE MAC introduced a new Prioritized Contention Access () for transfer of time-critical packets with lower channel access latency compared to CMA/CA. In this paper, we first propose a novel Markov chain based analytical model for unslotted CMA/CA and for industrial applications. The unslotted model is further extended to derive the analytical model for slotted CMA/CA and. Primary emphasis is laid on understanding the performance of compared to CMA/CA for different traffic classes in industrial applications. The performance analysis shows the slotted achieves a reduction of 63.3% and 97% in delay and power consumption respectively compared to slotted CMA/CA, whereas unslotted achieves a delay reduction of 53.3% and reduction of power consumption by 96% compared to unslotted CMA/CA without any significant loss of reliability. The proposed analytical models for both slotted and unslotted IEEE MAC offer satisfactory performance with less than 5% error when validated using Monte Carlo simulations. Also, the performance is verified using real-time testbed. Index Terms Industrial Internet of Things, IEEE , CMA/CA, Prioritized Contention Access, Markov chain I. ITRODCTIO In recent years, industrial applications such as monitoring, controlling, automation, etc., have witnessed a significant increase in usage of the Internet of Things (IoT) technologies for communication [] [3], especially IEEE [4], [5]. Also, a new Prioritized Contention Access () is introduced in IEEE MAC to provide service differentiation in IoT applications [6]. Transfer of prioritized or critical data with low latency plays a crucial role in industrial monitoring and automation applications [7], [8]. The existing IEEE e supports time-slotted channel hopping (TCH) where the assigned time slots are used for communication between the nodes, and frequency hopping is used to mitigate the effects of fading [9]. Traditional CMA/CA suffers from increased channel access delay with an increase in traffic or number of nodes. nlike CMA/CA, offers faster channel access without any significant loss of reliability. Hence, a time-critical packet uses and CMA/CA for normal packet transmission. In this paper, using Markov chains, we model the CMA/CA and in both beacon-enabled and nonbeacon-enabled personal area network (PA) and derive the performance metrics (reliability, delay, and power consumption). Our primary contributions in this paper include: The authors are with the Department of Electrical Engineering, Indian Institute of Technology Hyderabad, Hyderabad 52285, India ( ee2m2@iith.ac.in; raji@iith.ac.in). Mathematical formulation for analyzing the performance of unslotted and CMA/CA in a nonbeacon-enabled PA. Mathematical formulation for analyzing the performance of slotted and CMA/CA in a beacon-enabled PA. Validation of proposed analytical models for both slotted and unslotted channel access using a real-time testbed and Monte Carlo simulations. Performance comparison of and CMA/CA in both beacon-enabled and nonbeacon-enabled PA. Rest of this paper is organized as follows. ections II discusses the existing studies, and ection III provides the brief description of contention based random channel access schemes in IEEE standard respectively. ection IV provides the mathematical formulation for nonbeacon-enabled PA, and mathematical formulation for beacon-enabled PA is discussed in ection V. Performance and validation of proposed analytical models using Monte Carlo simulations and real-time testbed are provided in ection VI. Finally, section VII concludes the paper by discussing the future scope of this work. II. RELATED ORK Accurate analytical models of this kind aid in understanding the performance and suitability of channel access mechanisms and aid in optimizing the operational parameters leading to efficient network operation. Many studies to analyze the performance of IEEE CMA/CA exist [] [8] and very few studies analyzed the performance of. Authors in [] and [] used event chains and Markov models respectively to analyze slotted CMA/CA but the performance of is not considered. In [2], authors analyzed the performance of dense traffic multi-hop networks. In [3], Pollin et al. considered star topology under saturated and unsaturated traffic conditions without retransmissions. The models proposed in [4] [6] analyzed the impact of CMA/CA parameters, the number of nodes, and data frame size on the network throughput and energy efficiency, but do not discuss the performance of. Although in this study we did not consider throughput as a performance metric, one can refer to [5] to extend this model to derive the throughput. In [7], [8], authors analyzed the performance of IEEE MAC considering the effects of noisy environments and channel fading but do not consider. Gebremedhin et al. in [9] analyzed the performance of using only simulation model and no analytical model is considered. In [2] and [2], the authors investigated the (c) 28 IEEE. Personal use is permitted, but republication/redistribution requires IEEE permission. ee for more information.

2 This article has been accepted for publication in a future issue of this journal, but has not been fully edited. Content may change prior to final publication. Citation information: DOI.9/TII , IEEE 2 TABLE I: ummary of primary notations used for modeling Parameter η h p L c L s L p L ack n m macminbe macmaxbe τ P Q b, b i,k b i,k,j p i,k τ RCMA RCMA DCMA DCMA PCMA PCMA P fr P fc P de P dc Description Probability of at least one packet availability in the queue Probability of the available packet being time critical Packet collision duration uccessful packet duration Packet duration Acknowledgment duration Max. no. of retries o. of backoff stages Min. backoff exponent Max. backoff exponent CCA busy probability CCA2 busy probability Probability for collision Probability of a node in CCA o. of nodes in the network Probability of the node residing in Idle state Probability of node residing in the state (,) of unslotted CMA/CA Probability of unslotted CMA/CA states Probability of slotted CMA/CA states Probability of states Probability of node attempting CCA in an arbitrary time Reliability of unslotted CMA/CA Reliability of slotted CMA/CA Delay of successfully transmitted packet using unslotted CMA/CA Delay of successfully transmitted packet using slotted CMA/CA Power consumption of unslotted CMA/CA Power consumption of slotted CMA/CA Probability of normal packet discard due to exceeded retransmissions Probability of normal packet discard due to channel access failure Probability of packet being discarded due to delay expiry in Probability of packet being discarded due to collision in performance of frame slotted aloha for low energy critical infrastructure monitoring (LECIM) applications. Hence to the best of our knowledge, this is the first study which provides the theoretical model for the behavior of along with CMA/CA in both beacon-enabled and nonbeacon-enabled PA. III. COTETIO BAED RADOM CHAEL ACCE MECHAIM I IEEE TADARD The Personal Area etwork (PA) using IEEE MAC supports both beacon-enabled and nonbeaconenabled operation. In a beacon-enabled PA, the node waits for a periodic beacon from the coordinator and synchronizes to the superframe structure after which it employs either slotted CMA/CA or slotted for the channel access. lotted is chosen whenever a time-critical packet needs to be transmitted. hereas in the nonbeacon-enabled PA, the coordinator does not transmit any beacon and the nodes use unslotted CMA/CA or unslotted for transmission depending on the packet criticality. lotted? TB = TB TB =? BE=max(,macMinBE-) BE=max(,macMinBE-) TB = random(2 BE -) TB = random(2 BE -) delay = C = C delay = delay = delay+ delay = delay+ delay> critdelay Perform CCA Channel idle? uccess Failure TB = TB delay> critdelay Locate backoff boundary Perform CCA Channel idle? TB =? C = C C =? uccess Failure Fig. : Operation of slotted and unslotted the validity of data expires. Then the node selects a backoff waiting time (TB) randomly chosen from [,2 BE ] where BE = max(,macminbe ) and macminbe is the minimum backoff exponent. A backoff period in IEEE lasts for a duration of 2 symbols (i.e., 32µs). The node continuously monitors the channel and decrements T B by one only if the channel is free. After every channel sensing, the node updates the delay and discards the packet if the node does not get channel access before the specified critdelay. This process continues until the node gets access to the channel after TB =. In slotted, the backoff boundaries of all the nodes are aligned with the start of the periodic superframe, and channel sensing is performed at the beginning of a backoff boundary. Also, slotted uses Contention idth (C ) equals to C where the node performs CCA successively and transmits the packet only if the channel is free during the entire period of the C. sually C is two backoff periods, and once the node finishes backoff waiting (TB = ), the node performs CCA and decrements C if the channel is clear, and proceeds to transmission if C=. If the channel is found busy during the C, C is reset to C, and the node repeats the same process. The slotted uses acknowledgments received from coordinator to make sure the packet is transmitted successfully. A. Prioritized Contention Access Mechanism () Fig. describes the channel access flow using both slotted and unslotted. Initially, a delay counter is started on the arrival of a time-critical packet which updates after every Clear Channel Assessment (CCA) performed. critdelay is the maximum delay specified by the application within which the time critical data needs to be transmitted after which B. Carrier ense Multiple Access - Collision Avoidance (CMA/CA) At the beginning of the unslotted CMA/CA, TB is initialized to a value randomly chosen from [, ) where = 2 macminbe. After the backoff waiting, the node performs CCA and starts transmission if the channel is free else it increments the BE (BE=BE+) and selects a random backoff from (c) 28 IEEE. Personal use is permitted, but republication/redistribution requires IEEE permission. ee for more information.

3 This article has been accepted for publication in a future issue of this journal, but has not been fully edited. Content may change prior to final publication. Citation information: DOI.9/TII , IEEE 3 [, ), where = 2 min(macmaxbe,be) andmacmaxbe is maximum backoff exponent. The node repeats the same process until the number of backoff stages ( B) exceeds the specified maximum backoff stages (macm axbackof f s) after which the packet is discarded. imilar to unslotted, unslotted CMA/CA employs no acknowledgment (ACK), whereas the slotted CMA/CA relies on acknowledgment (ACK). Also, slotted CMA/CA employs contention width C = C. As CMA/CA is well studied in the literature, we advise the readers to refer [6], for a more detailed operation of CMA/CA. hile the nonbeacon-enabled channel access is decentralized, improves throughput, and reduces the delay, the beaconenabled channel access is complex as the nodes require tight synchronization with the beacon superframe. The channel access in slotted mode requires performing CCA for a C of 2 which helps in the detection of ACK transmission by the gateway. hereas in the case of unslotted channel access the CCA is performed only once which increases collisions if ACK is employed. Also, usage of ACK leads to increased energy consumption [4], [22]. Hence, in this study, unslotted channel access is used with no acknowledgments (ACK), meaning that if a collision occurs, the transmitting node still proceeds to serve a new packet. For the mathematical formulation, we consider below acceptable assumptions which are in agreement with the existing popular studies in the literature. []. ) e assume the traffic overhead due to periodic beacon frame communication from the gateway is negligible. 2) Ideal channel conditions are considered. IV. MATHEMATICAL FORMLATIO FOR LEAF ODE OPERATIG I OBEACO-EABLED PA (IG LOTTED AD LOTTED CMA/CA) Fig. 2 shows the developed Markov chain model for unslotted CMA/CA with the node in the Idle state (Q) during the absence of packets. Each state in the Markov chain corresponds to a unit backoff period duration (2 symbols). η and h p represent the packet generation probability and the probability of the available packet being time-critical respectively. pon the availability of a normal packet with probability η( h p ), the node uses unslotted CMA/CA and selects a random backoff waiting time. These backoff waiting periods are represented using states (i,k), i [,m], k [, ) in the Markov chain. The states (i,), i [,m] represent the CCA. and indicate the probability of collision and channel being busy during the CCA respectively with L s and L c indicating the successful and collision packet lengths in terms of unit backoff periods. The states ( 2,k) and ( 3,k) represent packet collision and successful transmission states, whereas m represents the maximum backoff stages after which the packet is discarded due to channel access failure. Fig. 3 shows the Markov chain of used for timecritical packets with probability. The states are guided by a two-dimensional stochastic process (c(t), d(t)) where c(t) represents the backoff waiting counter and d(t) represents the delay incurred by the packet in terms of unit backoff period. 3, 2, Pc Pc Pc Pc Pc Pc 2,Lc 3,Ls Q,, m m, η η( hp),, m, m,, m,m Fig. 2: Markov chain model for unslotted CMA/CA 3, 2, -2,L c -3,L s -,, 2,, -,2,2 2,2,2 -,3,3 2,3,3 -,4,4 2,4,4 -,d,d 2,d,d,d,d 2,d,d Q η Fig. 3: Markov chain model for unslotted Hence, at the beginning of, the initial states that can be chosen, will all have the second dimension set to. upposing the node chooses backoff waiting time i, then it transits from the Idle state to (i,). After performing CCA, if the channel is found free the node transits from (i,) to (i,2) else it transits to (i, 2). In both the transitions, the second dimension is incremented as the node will have incurred with one backoff period delay in the previous state while performing CCA. This procedure continues until the node gets channel access within critdelay number of backoff periods and if the node incurs a delay equal to critdelay before accessing the channel, the packet is discarded. In the Markov chain, we represented the critdelay as d. Therefore, if the node reaches any of the states (i, d), the packet will be discarded, and the node transits to the Idle state. If the node gets channel access before critdelay, the node proceeds to transmission and the corresponding states are represented using ( 3, k) and ( 2, k) for both successful and collision respectively. One thing to note here is the state Q is common for both the Markov chains (unslotted CMA/CA in Fig. 2 and unslotted in Fig. 3). For clear discrimination between the states of CMA/CA and, we represent the CMA/CA state probabilities using b i,k and those of using p i,k. Table I summarizes the primary notations used for mathematical formulation. As Q is common for both unslotted and unslotted CMA/CA, P Q represents the probability of node residing in Q. From Fig. 2, the below transition probabilities can be formulated. P(i,k i,k+) =, i [,m], k [, i ), () (c) 28 IEEE. Personal use is permitted, but republication/redistribution requires IEEE permission. ee for more information.

4 This article has been accepted for publication in a future issue of this journal, but has not been fully edited. Content may change prior to final publication. Citation information: DOI.9/TII , IEEE 4 P(i,k i,k) =, i (,m], (2) P(Q m,) =, (3) P(,k Q) = η( hp), k [, ), (4) P( 3,k + 3,k) =, k [,L s ), (5) P( 2,k+ 2,k) =, k [,L c ), (6) P( 3, i,) = ( )( ), i [,m] (7) P( 2, i,) = ( )( ), i [,m], (8) P(Q 3,L s ) = P(Q 3,L c ) =. (9) Eq. () represents the probability of backoff counter decrement within the same backoff stage and (2) represents the probability of node proceeding to next backoff stage after the channel is sensed busy. Eq. (3) represents the node transiting to Idle state after the backoff expiry and (4) gives the probability of transition from Idle to CMA/CA and choosing the backoff waiting time k in the first backoff stage. Eqs. (5) and (6) express the probability of transition across the successful transmission and collision states respectively. Eqs. (7) and (8) represent the probability of node entering into successful and collision states from the last backoff period of backoff stage i respectively. Eq. (9) represents the probability of node transiting to Idle after both successful or collision transmission. imilarly, using Fig. 3, transition probabilities for unslotted can be computed as shown in ()-(5). P(i,k i,k ) =, i [,),k (,d], () P(i,k i,k ) =, i (,),k (,d], () P(i, Q) = ηhp, i [,), (2) P( 3,,k) = ( )( ), k [,d), (3) P( 2,,k) = ( ), k [,d), (4) P(Q i,d) =, i [,). (5) Eq. () represents the probability of an increase in delay within the same backoff counter which can only happen if the channel is busy due to which the delay increments without a change in the backoff counter. Eq. () gives the probability of decrement in backoff counter which happens when CCA in the state (i,k) is free and (2) gives the probability of time-critical packet arrival in Idle state and node selecting a random backoff slot in. Eqs. (3) and (4) represent the probability of node entering into successful and collision states from the last backoff period respectively. Eq. (5) represents the probability of node transiting to Idle after the critical delay expiry. sing these transition probabilities, we will now derive the individual state probabilities. (6) expresses the state probability b i,k in terms ofb, and the probabilityb, can be expressed in terms of P Q as shown in (7). ow combining (6) and (7), any CMA/CA backoff state probability can be expressed in terms of P Q as shown in (8). b i,k = i k i b i, = i k i i b,, (6) b, = P Q η( h p ), (7) b i,k = i k i i η( h p )P Q. (8) ow considering the CMA/CA transmission probabilities, the successful transmission state probability (b 3, ) can be expressed as. b 3, = ( )( ) m b i, = ( )( ) m i η( h p )P Q i= i= = ( )( m+ )P Q η( h p ). (9) imilarly, the collision state probability can be given as. m m b 2, = ( ) b i, = ( ) i η( h p )P Q i= i= = ( m+ )P Q η( h p ). (2) e now derive the rest of the state probabilities of from the Markov chain shown in Fig. 3, and the state probability p i,k can be expressed as { ( )p i+,k +p i,k, if i [, ),k (,d]) p i,k = p i,k, if i =,k (,d]. (2) The probability of a node selecting any of the random backoff states after a time-critical packet arrives can be given as p i, = PQηhp, i [, ]. (22) By making use of (2), (22) and exploiting the recursiveness, probability of any backoff state in can be formulated as below. p i,k = min( i,k ) k C j ( ) j k j P Q. (23) sing (23), the successful transmission probability (p 3, ) can be expressed as below. p 3, = ( )( ) d = ( )( ) d k= p,k k= min(,k ) k C j ( ) j k j P Q. Considering Fig. 2 and 3, by owing to chain regularities, the normalization criteria of this Markov chain can be given as P Q + m i b i,k + Ls i= + Ls b 3,k + Lc b 2,k p 2,k + p 3,k + Lc i= k= (24) d p i,k =. (25) Evaluating each summation term, the first summation term using (8) can be expressed as [ ] m i b i,k = PQη( hp) (2) m m+. (26) i= Considering the second summation term in (25) and by making use of (5) and (9), the simplified expression can be realized as below. L s b 3,k = L s ( )( m+ )P Q η( h p ). (27) ith the similar hypothesis used in deriving (27), we can (c) 28 IEEE. Personal use is permitted, but republication/redistribution requires IEEE permission. ee for more information.

5 This article has been accepted for publication in a future issue of this journal, but has not been fully edited. Content may change prior to final publication. Citation information: DOI.9/TII , IEEE 5 simplify the third summation term as below. L c b 2,k = L c ( m+ )P Q η( h p ). (28) The transmission probabilities for can be expressed as in (29) and (3). L s L c p 3,k = L s ( )( ) d min(,k ) p 2,k = L c ( ) d = L c ( ) d k= k= k C j ( ) j k j P Q, (29) p,k k= min(,k ) k C j ( ) j k j P Q. Finally, the sixth summation term is given by (3) i= k= d p i,k = d i= k= min( i,k ) (3) k C j ( ) j k j P Q. (3) By making use of (26)-(3) and the normalization criteria given by (25), P Q can be derived as below. P Q = { + η( hp) 2 [ (2) m+ 2 + m+ η( h p )(L s ( )+L c )( m+ )+ L s( )( ) d L c ( ) d d i= k= k= k= min(,k ) min(,k ) min( i,k ) ] + k C j ( ) j k j + k C j ( ) j k j + k C j ( ) j k j }. (32) The probability τ of a node attempting CCA in CMA/CA or attempting CCA in state (i,) of the mechanism can be given as τ = m b i, + d p,k. (33) i= sing (33), the channel busy probability can be given by (34). Equation (35) formulates the collision probability that at least one of the other ( ) nodes transmit the packet at the same time. k= = ( ( τ) )( )(L s ( )+L c ) = A. Reliability Model ( ( τ) )(L s( )+L c) +( ( τ) )(L, (34) s( )+L c) = ( ( τ) ). (35) The reliability of a node in a nonbeacon-enabled PA is defined as the fraction of generated packets that are successfully transmitted to the gateway. Eq. (36) gives the reliability of unslotted CMA/CA (R CMA ) where P fr and P fc indicate the packet failure due to collision and channel access failure within m+ backoff stages respectively.p fr in (37) gives the probability of a node getting the channel access but suffers due to collision and P fc in (38) gives the probability of a node not getting the channel access within the m+ backoff stages. R CMA = P fc P fr, (36) P fr = ( m+ ), (37) P fc = m+. (38) Reliability of unslotted (R ) is given by (39) where P de and P dc indicate the probability of a time-critical packet being discarded due to delay exceeding beyondcritdelay and packet lost due to collision respectively. R = P de P dc ( P de ). (39) The probability P de can be found using (4), where A g indicates the event that a time-critical packet was generated and event A d indicates that thus generated packet is discarded due to delay expiry. ProbabilityP dc which indicates the probability of collision is given by (4). P de = P(A d A g ) = P(Ad Ag) P(A g) = B. Delay Model = i= p i,d i= P Q min( i,d ) d C j( ) j d j, (4) P dc = ( ( τ) ). (4) The delay incurred for a successful packet transmission using unslotted CMA/CA or unslotted includes the delay for channel access and packet transmission time to the gateway. Equation (42) gives the average delay incurred in any given backoff stage i. The delay incurred by a successfully transmitted packet using CMA/CA in seconds (D CMA ) can be expressed as (43), where T b indicates the duration of a unit backoff period (32µs) and T C indicates the duration for sensing which is backoff period in unslotted CMA/CA. T s indicates the time taken for successful transmission (T b L s ). D CMA = T s +T b m D CMA,i = i [ i ( ) m+ i= k i, (42) (i+)t C + i D CMA,j ], (43) Considering the mechanism, delay incurred for the successful packet transmission in seconds can be expressed as below. D = T s +T b C. Power Consumption Model d kp,k k= d k= p,k. (44) The power consumption of the node modeled here comprises the power consumption of the radio in the Idle state, during channel access, and packet transmission, but do not consider the power consumed by the microcontroller. e (c) 28 IEEE. Personal use is permitted, but republication/redistribution requires IEEE permission. ee for more information.

6 This article has been accepted for publication in a future issue of this journal, but has not been fully edited. Content may change prior to final publication. Citation information: DOI.9/TII , IEEE 6 considered three power consuming states, idle during backoff waiting and in the Idle state (P i ), sensing during CCA (P sense ) and packet transmission (P tx ). Considering these three states, we express the total power consumption (P ) of the node using (45) and the power consumed in CMA/CA (PCMA ) and (P ) are given in (46) and (47) respectively. P = P i P Q +P CMA +P, (45) P CMA = P tx P = P tx [ Ls [ Ls b 3,k + Lc ] m b 2,k +P i i P i m p 3,k + Lc i= k= i i= k= b i,k + m b i,k +P sense b i,, (46) i= ] p 2,k +P sense i= k= d p i,k. (47) V. MATHEMATICAL FORMLATIO FOR LEAF ODE OPERATIG I BEACO-EABLED PA (IG LOTTED AD LOTTED CMA/CA) Fig. 4 provides the developed Markov chain model for a node using slotted and slotted CMA/CA where with a probability the node enters into and with probability η( h p ) chooses slotted CMA/CA. Each state in the developed Markov chain corresponds to a unit backoff slot duration (2 symbols). As the node enters into CMA/CA, the node selects a random backoff waiting time represented using states (i,k,j), i [,m], j [,n], k [, i ). pon the completion of backoff waiting, the node proceeds for Clear Channel Assessment (CCA, state (i,,j)) and if the channel is free, the node proceeds to CCA2 (state (i,,j)) and proceeds to transmission if free. and represent the probability of channel busy in CCA and CCA2 respectively. If CCA or CCA2 is busy in current backoff stage i, the node increments the backoff exponent and generates a backoff waiting time randomly chosen from [, i ]. This process is continued until the total backoff stages exceed the maximum backoff stages (m+) after which the packet is discarded due to channel access failure. tates ( 2, k, j), k [,L c ), j [,n] and( 3,k,j) k [,L s ), j [,n] represent the collision and successful transmission. L s and L c represent the successful packet transmission length (packet length (L p ) + Inter Frame pacing (IF) + ACK (L ack )) and collision length (L p + IF + ACK time-out duration). After collision, the node proceeds for retransmission and n represents the maximum allowed retransmissions beyond which node discards the packet. After a packet service, node checks for packet availability and if available chooses the appropriate channel mechanism else transits to Idle state. hile the states (,k), k [,d] and (,k), k [,d) represent CCA and CCA2, the states ( 3,k), k [,L s ] and ( 2,k), k [,L c ] represent successful and collision slots of. Eqs. (48) and (49) represent the transition probabilities from CCA of CMA/CA to successful and collision slots respectively, whereas (5) and (5) represent the transition probabilities from CCA of to successful and collision slots respectively. P( 3,,j i,,j) = ( )( )( ), i [,m], j [,n] (48) P( 2,,j i,,j)= ( )( ), i [,m], j [,n] (49) P( 3,,k) = ( )( )( ), k [,d) (5) P( 2,,k) = ( )( ), k [,d) (5) Here, we define a virtual state V which occurs after service completion by and CMA/CA for ease of mathematical formulation. From Fig. 4, the below transition probabilities can be inferred. From Fig. 4, the virtual state probability (P V ) can be expressed as P V = p,d + i= p i,d +p 3,Ls +p 2,Lc + b 2,Lc,n + n b 3,Ls,j + n b m,,j (+( )). (52) The Idle state probability (P Q ) can be expressed as P Q = P Q ( η)+p V ( η) = P V η η. (53) The probability p i, in terms of P V can be formulated as p i, = P V +P Q ηhp = P V hp, (54) where i [, ]. ith similar hypothesis, the probability P i,2 can be given as { pi, +( )p i+,, if i [, 2] p i,2 = (55) p i,, if i =. pon generalizing, the probability p i,k can be given by p i,k = min( i,k ) k C j ( ) j k j P V h p, i [, ], j [,d]. (56) imilarly, p,3 in terms of P V can be expressed as p,3 = p,2 +( )p,2 +p,2 = ( )p, + ( )(p, +( )p 2, )+(p, +( )p, ) PV hp = ( ) = F PV hp,3(,), (57) where F,3 is function of and. In similar way the probabilities p,k for k [,d] and p,k for k [2,d] can be expressed as below p,k = F,k (,) PV hp, k [,d], (58) p,k = ( )p,k, k [2,d]. (59) ow, the success and collision probabilities of are p 3, = ( )( ) d p,k, (6) k=2 d p 2, = ( ) p,k. (6) k= (c) 28 IEEE. Personal use is permitted, but republication/redistribution requires IEEE permission. ee for more information.

7 This article has been accepted for publication in a future issue of this journal, but has not been fully edited. Content may change prior to final publication. Citation information: DOI.9/TII , IEEE 7 η Q η( h p) η η( h p) Virtual state V 2, -2,Lc,,2,3,d 2,d - 3, -3,Ls -,, 2,,,,,,,, P c,2,2 2,2,2 -P -3,Ls-, c,,,,,,,3,3 2,3,3-3,, m - m,, m,, m,,,4,4 2,4,4-3,Ls-,n,d,d,d,d Markov chain model for 2,d 2,d,d,d -3,,n ,,,,n,,n -2,Lc-,,,n,,n m m,,n m,,n,,n,,n m,,n m m,-,,-, m,m-,n,-,n,-,n m,m-,n -2,,n -2,Lc-,n Markov chain model for CMA/CA Fig. 4: Proposed Markov chain model for slotted CMA/CA and channel access mechanisms of IEEE Considering the CMA/CA Markov chain, the probability of a node residing in state (,,) can be expressed as b,, = η( h p )P V +η( h p )P Q = ( h p )P V. (62) sing (62), the probability of i consecutive channel access failure can be found using (63) b i,, = (+( )) i b,, = x i b,,, (63) where x = (+( )) represents the channel access failure probability in any backoff stage. imilarly the probability for a node to retransmit can be given as b,,j = ( ( x m+ )) j b,, = y j b,,, j [,n], (64) where y = ( x m+ ) indicates the probability for node getting channel access withinmbackoff stages and occurrence of a collision. The successful and collision state probabilities in CMA/CA can be given as in (65) and (66) respectively. b 3,,j = ( )( x m+ )b,,j, j [,n], (65) b 2,,j = ( x m+ )b,,j, j [,n]. (66) The normalization property can now be expressed as P Q + m n i= k= i i= k= d p i,k + d b i,k,j + n k=2 ( Ls p,k + Ls p 3,k + Lc p 2,k + b 3,k,j + Lc ) b 2,k,j =. (67) sing (56) and (58), the first summation term in terms of P V can be written as i= k= d p i,k = d d i= k= k= min( i,k ) PV hp F,k (,) + k C j ( ) j k j P V h p = P V, and using (59), the second summation term can be given as d p,k = ( ) d k=2 k=2 PV hp F,k (,) = 2P V. (69) (68) sing (6) and (6), the third and fourth summation terms can be expressed as (7) and (7) respectively. L s p 3,k = L s ( )( )( ) d l=2 PV hp F,l (,) = 3 P V, (7) (c) 28 IEEE. Personal use is permitted, but republication/redistribution requires IEEE permission. ee for more information.

8 This article has been accepted for publication in a future issue of this journal, but has not been fully edited. Content may change prior to final publication. Citation information: DOI.9/TII , IEEE 8 L c p 2,k = L c ( )( ) d l=2 PV hp F,l (,) = 4P V. (7) Considering the fifth summation term, using (62), (63) and (64) it can be expressed as m n i i= k= = PV ( hp) 2 b i,k,j = m ( +( ) xm+ x n i i= b i,k,j + m (2x) m+ 2x + xm+ x n b i,,j i= ) y n+ y y n+ y ( h p )P V = 5 P V. (72) Finally, by using (65) and (66) the sixth summation can be formulated as n ( Ls b 3,k,j + Lc b 2,k,j ) = (L s ( )+L c )( x m+ ) yn+ y ( h p )P V = 6 P V. (73) By substituting (68) - (73) in (67), P V can be derived as ( P V = η η ). (74) Probability of a node attempting CCA in any given random time (τ) can be given as τ = m i= n b i,,j + d b,k. (75) k= sing (75), the probability of collision is = ( τ). (76) as given by (77), comprises of channel busy due to packet transmission ( ) and due to acknowledgment ( 2 ) which are expressed in (78) and (79). = + 2, (77) = L p ( ( τ) )( )( ), (78) 2 = L ack τ( τ) ( τ) ( ( τ) )( )( ). (79) imilarly can be derived as (8) and for more detailed derivation of, one can refer to []. A. Reliability Model = ( τ) +τ( τ) 2 ( τ) +τ( τ). (8) The reliability of a node in a beacon-enabled PA is defined as the fraction of generated packets that received the acknowledgment successfully. Reliability of slotted (R ) is given in Eq. (8), where P de and P dc indicate the probability of a time-critical packet being discarded due to delay exceeding beyond d and packet loss due to collision respectively. R = P de P dc ( P de ). (8) The probability P de can be found using Eq. (82), where A g indicates the event that a time-critical packet was generated and event A d indicates the generated packet is discarded due to delay expiry. ProbabilityP dc which indicates the probability of collision is given by Eq. (83) P de = P(A d A g ) = P(A d A g) P(A g) = = i= min( i,d ) p,d + p i,d i= P Q d C k ( ) k d k, (82) P dc = ( ( τ) ). (83) Packet losses in CMA/CA occur due to exceeded retransmissions and packet discard due to the exceeded maximum number of backoff stages. Hence the reliability of slotted CMA/CA (R CMA ) can be expressed as (84) where P fc and P fr indicate the packet failure due to channel access failure within m + backoff stages and exceeded retransmissions respectively. R CMA = P fc P fr, (84) B. Delay Model P fc = xm+ ( y n+ ) y, (85) P fr = y n+. (86) The delay incurred for a successful packet transmission using slotted CMA/CA or slotted includes the delay for channel access, packet transmission time to the gateway and time taken for the reception of acknowledgment from the gateway. Delay incurred for a successful packet transmission using can be expressed as below. D = T s +T b d kp,k ( ) k= d p,k ( ) k=, (87) where T b is the length of a unit backoff period which is 32µs and T s indicates the time taken for successful transmission (T b L s ). e make use of delay incurred for a successful transmission using CMA/CA in [] and is given by (88) ( ) D CMA = T s +E[ T h ]+ y y (n+)yn+ y n+ (T c +E[ T h ]). (88) where E[ T h ] indicates the approximate backoff delay given by (89), T c indicates the time taken for successful transmission (T b L c ) and γ = max(,( )). As deriving (88) and (89) is not our primary contribution in this paper, we advise the readers to refer [] for more insights. ( ( E[ T h ] = 2T b (+ 4 γ γ m+ 3(m+)γ m+ γ C. Power Consumption Model (2γ) 2 m+ 2γ ) + 3γ γ ( +) ), (89) The power consumption of the node modeled here comprises the power consumption of the radio in the Idle state, (c) 28 IEEE. Personal use is permitted, but republication/redistribution requires IEEE permission. ee for more information.

9 This article has been accepted for publication in a future issue of this journal, but has not been fully edited. Content may change prior to final publication. Citation information: DOI.9/TII , IEEE 9 TABLE II: Average power consumption of node in different states considered for analysis tate Avg. Power Consumption (µ) P i 6 P tx 6 P rx 7 P sense 7 during channel access, packet transmission, and acknowledgment reception, but do not consider the power consumed by the microcontroller. Assuming P i, P tx, P rx and P sense indicate the power consumption of the node in idle mode, transmit, receiving and sensing mode respectively, total power consumed (Ptot ) comprises of power consumption while node spends in Idle state, during mechanism (P ) and CMA/CA (PCMA ). P tot = P ip Q +P +P CMA, (9) The power consumed in states can be calculated as below P = P sense 2 +P i ( i= i= 3 d p i,k + d k= k=2 p,k ) +P tx 2 L p p i,k i= 3 L p+l ack+ p i,lp + (P rx p 3,k +P i p 2,k ), (9) k=l p+ and power consumed in CMA/CA states can be found using (92) P CMA = P i m i i= k= 2 +P tx L p i= 3 + n n m n b i,k,j +P sense (b i,,j +b i,,j ) n 2 b i,k,j +P i L p+l ack+ k=l p+ i= n b i,lp,j i= 3 VI. PERFORMACE AALI (P rx b 3,k,j +P i b 2,k,j ). (92) For the performance analysis, a star topology with nodes and a gateway is considered. Authors in [23], proposed a simplistic Monte Carlo simulation model with ideal channel conditions using C, for analyzing the performance of MAC layer. e extended the simulation model proposed in [23] to analyze the performance of in co-existence with CMA/CA. Primary assumptions in the simulation framework developed include: Traffic due to periodic beacon frame communication is negligible. Ideal channel conditions are considered. Also, we developed a real-time testbed for analyzing the realtime performance of the proposed models. e made use of commercially available IITH Motes which support Contiki 3. for the development of the testbed [24]. Each experiment comprises a fixed number of nodes deployed within line of sight range in a star topology inside a room of dimensions 7.5m x m. In [7], authors analyzed the effects of channel fading on the performance of IEEE MAC and claims the negative effect of fading on the reliability when the distance between the nodes increase beyond m. As the proposed analytical models aims at analyzing the performance of MAC layer under ideal channel conditions, we have closely deployed the nodes thereby minimizing the effects of channel conditions such as fading. Also, for validating with the experimental outcomes, we consider reliability, delay and ignore the power consumption because the power consumption of the mote includes the power consumed by the microcontroller and the radio. hereas when comparing with the simulation outcomes, we considered all the three parameters reliability, delay and power consumption. Each experiment is conducted for 3 minutes, and the performance measures provided in this paper are average taken over measurements acquired from the randomly selected leaf node every 2 seconds. e have considered two different classes of prioritized data in industrial applications with critical delays of 2.5ms and 5ms each [25] and TABLE II gives the power consumption of node in different states considered for analyzing the performance [24]. A. Performance of nonbeacon-enabled PA (ses unslotted and CMA/CA) Fig. 5(a) plotsr and R CMA versusη for = 2 and 4 with d = 8 backoff periods (2.5ms). ith an increase in η, traffic and channel congestion in the PA increases. It also increases the chances for the delay in accessing the channel to exceed d leading to a dominant loss of time-critical packets and increases number of packet collisions. Hence, unslotted CMA/CA offers better reliability compared to unslotted. By increasing from = 2 to 4 the traffic further increases resulting in more loss of packets due to channel access failure leading to further degradation in reliability of CMA/CA and. Fig. 5(b) plots the DCMA and D for d = 8, and one can observe the significant difference between delay offered by CMA/CA and. offers a very lower delay compared to CMA/CA as the channel access is faster. Also, the maximum delay for channel access of a node using will be d. ith an increase of η, the latency incurred for channel access increases and the same behavior will incur by increasing. Fig. 5(c) plots the power consumption of and CMA/CA where the power consumed by for both = 2 and = 4 are very lower compared to CMA/CA. As the number of nodes increase, the latency incurred for channel access increases due to which the power consumed by CMA/CA is less for = 2 compared to the = 4 scenario. As we increase the d, chances for channel access using increases thereby increasing R and the same can be seen from Fig. 5(d) for d = 6 backoff periods (5ms). The reliability offered by is almost identical to that of CMA/CA for both = 2 and = 4. ith the identical reliability of and CMA/CA, major advantage of using can be observed from delay and power consumption as shown in Fig. 5(e) and 5(f) respectively. Fig. 5(e) plots DCMA andd ford = 6 where thed is very lower compared to CMA/CA. imilarly, the power consumption of and CMA/CA for d = 6 is shown in Fig. 5(f) where P is negligible when compared to P CMA. Also, (c) 28 IEEE. Personal use is permitted, but republication/redistribution requires IEEE permission. ee for more information.

10 This article has been accepted for publication in a future issue of this journal, but has not been fully edited. Content may change prior to final publication. Citation information: DOI.9/TII , IEEE.5 R -im (=2) R -Ana (=2) R -Exp (=2) R CMA -im (=2) R -Ana (=2) CMA R -Exp (=2) CMA R -im (=4) R -Ana (=4) R -Exp (=4) R -im (=4) CMA R -Ana (=4) CMA R CMA -Exp (=4) D -im (=2) D -Ana (=2) D -Exp (=2) D CMA -im (=2) D CMA -Ana (=2) D -Exp (=2) CMA D -im (=4) D -Ana (=4) D -Exp (=4) D -im (=4) CMA D CMA -Ana (=4) D -Exp (=4) CMA P -im (=2) (a) Effect of η, on R CMA, R (d = 2.5ms) (b) Effect of η, on DCMA, D (d = 2.5ms) (c) Effect of η, on PCMA, P (d = 2.5ms) P -Ana (=2) P CMA -im (=2) P. -im (=2).8 P -Ana (=2) P -im (=2) CMA P -Ana (=2) CMA P -im (=4) P -Ana (=4) P CMA -Ana (=2) P -im (=4) P -Ana (=4) P -im (=4) CMA P -Ana (=4) CMA P -im (=4) CMA P -Ana (=4) CMA R -im (=2) R -Ana (=2) R -Exp (=2) R CMA -im (=2) R CMA -Ana (=2) R CMA -Exp (=2) R -im (=4) R -Ana (=4) R -Exp (=4) R -im (=4) CMA R -Ana (=4) CMA R -Exp (=4) (d) Effect of η, on R CMA, R (d = 5ms) R -im (=2) R -Ana (=2) R -Exp (=2) R CMA -im (=2) R CMA -Ana (=2) R CMA -Exp (=2) R -im (=4) R -Ana (=4) R -Exp (=4) R -im (=4) CMA R -Ana (=4) CMA R -Exp (=4) (e) Effect of η, on DCMA, D (d = 5ms) (f) Effect of η, on PCMA, P (d = 5ms) Fig. 5: Effect of η and on R CMA, R, D CMA, D, P CMA and P. Model parameters: L p = L s = L c = 6 backoff periods (6 bytes), h p =., macminbe = 3, m = 5, macmaxbe = 8 when compared to d = 8, in the case of d = 6, as more packets are being transmitted using the node performs CCA for more times due to which there is a little increase in delay for packet transmission and power consumption. In the case of CMA/CA, since the generation traffic remained same, RCMA, D CMA and P CMA remained almost the same although d is increased. From the performance analysis, it is observed that unslotted achieves average delay reduction of 53.3% and an average reduction in power consumption by 96% compared to unslotted CMA/CA. B. Performance of beacon-enabled PA (ses slotted and CMA/CA) Fig. 6(a) plotsr and R CMA versusη for = 2 and = 4 with a d of 8 backoff slots (2.5ms). imilar to the case of nonbeacon-enabled as η increases, the traffic and channel congestion in the PA increases.it also increases the chances for the delay in accessing the channel to exceed d leading to a dominant loss of time-critical packets. Hence slotted CMA/CA offers significantly better reliability compared to slotted. hen compared to the reliability of unslotted, as the node using slotted needs to perform CCA for C = 2 consecutively, the opportunities for accessing channel further reduces compared to unslotted leading to significant increase in packet failure due to delay expiry. By increasing from = 2 to = 4 the traffic further increases resulting in more loss of packets due to channel access failure leading to further degradation of reliability for both CMA/CA and. Fig. 6(b) plots the DCMA and D for d = 8 and one can observe the significant difference between delay offered by CMA/CA and. imilar to unslotted scenario, slotted offers a very lower delay compared to slotted CMA/CA as the channel access is faster and the maximum delay for channel access of a node using will be d. ith increase in η, the channel congestion increases and hence the latency incurred for channel access increases and the same behavior will incur with increase in. Fig. 6(c) plots the power consumption of and CMA/CA where the power consumed by for both = 2 and = 4 are very lower compared to the power consumed by CMA/CA. As number of nodes increase, the latency incurred for channel increases due to which the power consumed by CMA/CA for = 2 compared to = 4 scenario. Although the node performs channel assessment for C period before accessing the channel, it can at maximum perform 8 CCAs before accessing the channel in both slotted and unslotted for d = 8, due to which the power consumption and delay are nearly identical. One can also observe the same from Fig. 6(b) and 6(c) with delay and power consumption of slotted respectively which are identical to that of unslotted. As we increase the d, opportunities for the node to access the channel using increases thereby increasing R and the same behavior can be seen from Fig. 6(d) for d = 6 backoff slots (5ms). ith d = 6 the reliability offered by is slightly lesser than that of CMA/CA for both = 2 and = 4 due to the fact that CMA/CA has feasibility for additional retransmission (n = ). Regarding delay and power consumption still outperforms CMA/CA as shown in fig. 6(e) and 6(f) respectively. Fig. 6(e) plots the DCMA and D for d = 8 where the D is very lower compared to CMA/CA. imilarly, the power consumption of and CMA/CA for d = 6 is shown in Fig. 6(f) and the power consumed by is negligible when compared with CMA/CA. Also, when compared to d = 8, in the case of d = 6, as more packets are being transmitted using the node performs CCA for more times due to which there is a little increase in delay for packet transmission and power consumption. In the case of CMA/CA, since (c) 28 IEEE. Personal use is permitted, but republication/redistribution requires IEEE permission. ee for more information.

11 This article has been accepted for publication in a future issue of this journal, but has not been fully edited. Content may change prior to final publication. Citation information: DOI.9/TII , IEEE D -im (=2) D -Ana (=2) D -Exp (=2) D CMA -im (=2) D -Ana (=2) CMA D CMA -Exp (=2) D -im (=4) D -Ana (=4) D -Exp (=4) D -im (=4) CMA D CMA -Ana (=4) D CMA -Exp (=4). P -im (=2) P -Ana (=2) P -im (=2) CMA P CMA -Ana (=2) P -im (=4) P -Ana (=4) P -im (=4) CMA P -Ana (=4) CMA R -im (=2) R -Ana (=2) R -Exp (=2) R CMA -im (=2) R CMA -Ana (=2) R CMA -Exp (=2) R -im (=4) R -Ana (=4) R -Exp (=4) R CMA -im (=4) R CMA -Ana (=4) R CMA -Exp (=4) (a) Effect of η, on R CMA, R (d = 2.5ms) (b) Effect of η, on DCMA, D (d = 2.5ms) (c) Effect of η, on PCMA, P (d = 2.5ms) D -im (=2) D -Ana (=2) D -Exp (=2) D CMA -im (=2) D CMA -Ana (=2) D -Exp (=2) CMA D -im (=4) D -Ana (=4) D -Exp (=4) D -im (=4) CMA D CMA -Ana (=4) D -Exp (=4) CMA.5. P -im (=2) P -Ana (=2) P CMA -im (=2) P -Ana (=2) CMA P -im (=4) P -Ana (=4) P -im (=4) CMA P -Ana (=4) CMA R -im (=2) R -Ana (=2) R -Exp (=2) R -im (=2) CMA R -Ana (=2) CMA R CMA -Exp (=2) R -im (=4) R -Ana (=4) R -Exp (=4) R CMA -im (=4) R -Ana (=4) CMA R -Exp (=4) CMA (d) Effect of η, on R CMA, R (d = 5ms) (e) Effect of η, on DCMA, D (d = 5ms) (f) Effect of η, on PCMA, P (d = 5ms) Fig. 6: Effect of η and on R CMA, R, D CMA/CA, D, P CMA and P. Model parameters: L p = 6 backoff periods (6 bytes), L ack = backoff period ( bytes), L s = L c = 8 backoff periods, h p =., macminbe = 3, m = 5, macmaxbe = 8, n = the generation traffic remained same, RCMA, D CMA and PCMA remained almost the same although d is increased. Table III shows the performance with variation in h p for both beacon-enabled and nonbeacon-enabled PA using the proposed analytical models. Although h p varies, the underlying amount of traffic generated (η) is kept unchanged due to which one can observe a very little degradation in R, R CMA, D, D CMA, R, R CMA, D and DCMA. hereas P CMA, P CMA decrease and P, P increase as more packets use compared to CMA/CA. From the performance analysis, it is observed that slotted achieves average delay reduction of 63.3% and average reduction in power consumption by 97% when compared to slotted CMA/CA. Each simulation outcome is the average taken over realizations with each realization having a simulation length of 28 seconds. e have also indicated the 95% confidence intervals, and the analysis shows that the proposed Markov chain and mathematical formulation models the IEEE MAC layer accurately by achieving less than 5% error when compared with both the experimental and simulation outcomes. VII. COCLIO In this paper, we proposed a novel analytical model to analyze the performance of IEEE MAC layer for both beacon-enabled and nonbeacon-enabled PA. e developed a Markov chain and mathematical formulation of reliability, delay for successful packet transmission and power consumption of the node when using unslotted, slotted, unslotted CMA/CA and slotted CMA/CA. Also, a real-time testbed using commercially available IITH Motes with Contiki 3. is developed for analyzing the performance of the proposed analytical models. Validation of the proposed models using both the Monte Carlo simulations and realtime testbed shows that the proposed models analyze the performance of the network accurately by achieving less than 5% error. Also, the service differentiation offered by mechanism when used for transmission of time-critical packets is emphasized. It is observed that achieves average delay reduction of 63.3% and 53.3% compared to CMA/CA in beacon-enabled and nonbeacon-enabled PA respectively without any significant loss of reliability. also achieves an average reduction in power consumption by 97% and 96% compared to CMA/CA in beacon-enabled and nonbeaconenabled PA respectively. To the best of our knowledge, this is the first study which analyzes the performance of when operated simultaneously along with CMA/CA in both beacon-enabled and nonbeacon-enabled using an accurate analytical model. e are convinced that the model can significantly aid in the development of optimization techniques to improve the network operational efficiency. As a future scope of this work, we would like to develop and model an efficient MAC protocol mainly for industrial applications which supports multiple classes of prioritized data with different critical delay requirements considering the channel conditions. ACKOLEDGMET This work is jointly supported by Visvesvaraya PhD cheme, Ministry of Electronics and Information Technology (MEIT, Govt. of India) and Indian Institute of Technology Hyderabad, India REFERECE [] M. ollschlaeger, T. auter and J. Jasperneite, The Future of Industrial Communication: Automation etworks in the Era of the Internet of (c) 28 IEEE. Personal use is permitted, but republication/redistribution requires IEEE permission. ee for more information.